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[[:Category:Complex analysis|Complex analysis]] | [[:Category:Geometry|Geometry]] | ...

* [[Hurwitz's theorem (complex analysis)]] * [[Riemann–Hurwitz formula]] in algebraic geometry ...

{{short description|Extension of the Schwarz lemma for hyperbolic geometry}} ...–Pick''' theorem is an extension of the [[Schwarz lemma]] for [[hyperbolic geometry]], such as the [[Poincaré half-plane model]]. ...

...on rationality for surfaces''' is a classical result of [[Max Noether]] on complex [[algebraic surface]]s, giving a criterion for a [[rational surface]]. Let *[[List of complex and algebraic surfaces]] ...

Several theorems are named after [[Augustin-Louis Cauchy]]. '''Cauchy theorem''' may mean: *[[Cauchy's integral theorem]] in complex analysis, also [[Cauchy's integral formula]] ...

...are the curves.<ref>James S. Milne, ''Jacobian Varieties'', Corollary 12.2 in {{Harvtxt|Cornell|Silverman|1986}}</ref> ...rieties]], is [[injective]] (on [[geometric point]]s). Generalizations are in two directions. Firstly, to geometric questions about that morphism, for ex ...

...space|compact]] [[Kähler manifold]]s. In effect it says precisely which [[complex manifold]]s are defined by [[homogeneous polynomial]]s. ...'' cohomology class, there is a complex-analytic embedding of ''M'' into [[complex projective space]] of some high enough dimension ''N''. ...

...o [[Function of several complex variables|several complex variables]], and in the general development of [[sheaf cohomology]]. Theorem B is stated in cohomological terms (a formulation that Cartan ([[#CITEREFCartan1953|1953]] ...

...erential geometry]] topics. See also [[glossary of differential and metric geometry]] and [[list of Lie group topics]]. ==Differential geometry of curves and surfaces== ...

In [[mathematics]], a '''classification theorem''' answers the [[classificatio ...p in solving it. (A combination of invariant values is realizable if there in fact exists an object whose invariants take on the specified set of values) ...

{{short description|One of several theorems in different areas of mathematics}} ...ry]], '''Schur's theorem''' is a theorem of [[:de:Axel Schur|Axel Schur]]. In [[functional analysis]], '''Schur's theorem''' is often called [[Schur's pr ...

...tics]], the '''Castelnuovo–de Franchis theorem''' is a classical result on complex [[algebraic surface]]s. Let ''X'' be such a surface, projective and [[Algeb ...ation|title=Geometry and Complex Variables|volume=132|series=Lecture Notes in Pure and Applied Mathematics|first=S.|last=Coen|publisher=CRC Press|year=19 ...

{{Short description|Concept in geometry}} ...by the two [[ray (geometry)|rays]] between the vertex and each [[endpoint (geometry)|endpoint]] of the segment. ...

In [[mathematics]], a smooth [[algebraic curve]] <math>C</math> in the [[complex projective plane]], of degree <math>d</math>, has [[Genus_(mathematics)#Top ...math> is any smoothly embedded connected curve representing the same class in [[homology (mathematics)|homology]] as <math>C</math>, then the genus <math ...

In [[mathematics]], the '''Hodge index theorem''' for an [[algebraic surface]] ...H'' be the [[divisor class]] on ''V'' of a [[hyperplane section]] of ''V'' in a given [[projective embedding]]. Then the intersection ...

...on|On the Euler characteristic of a holomorphic vector bundle on a compact complex manifold}} | field = [[Algebraic geometry]] ...

...' is a basic result of [[complex manifold]] theory and complex [[algebraic geometry]], describing general conditions under which [[sheaf cohomology]] groups wi == The complex analytic case == ...

...ion]]s, and the phrase '''Milnor fibration''' is more commonly encountered in the mathematical literature. These were introduced to study isolated singul ...on-constant [[polynomial function]] of <math>n+1</math> [[Complex analysis|complex variables]] <math>z_0,\dots,z_n</math> where the vanishing locus of ...

{{Short description|Theorem in plane geometry}} [[File:Van-Aubel-theorem combined.svg|thumb|The theorem can be applied to a complex (self-intersecting) quadrilateral.]] ...

{{Short description|On when a Riemannian manifold with sectional curvature in the interval (1, 4] is a sphere}} ...an the sectional curvature of every tangent 2-plane at each point must lie in <math>(1,4]</math>.) Another way of stating the result is that if <math>M< ...